Plasmas Meet Plasmonics Everything Old Is New Again

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Eur. Phys. J. D (2012) 66: 226 DOI: 10.1140/epjd/e2012-30273-3 THE EUROPEAN PHYSICAL JOURNAL D Colloquium

Plasmas meet plasmonics Everything old is new again

A.E. Rider1,2,K.Ostrikov1,2,a, and S.A. Furman1 1 Plasma Nanoscience Centre Australia (PNCA), CSIRO Materials Science and Engineering, P.O. Box 218, Lindﬁeld, 2070 New South Wales, Australia 2 Plasma Nanoscience @ Complex Systems, School of Physics, The University of Sydney, 2006 New South Wales, Australia

Received 26 April 2012 / Received in ﬁnal form 29 June 2012 Published online 4 September 2012 c The Author(s) 2012. This article is published with open access at Springerlink.com

Abstract. The term ‘plasmon’ was first coined in 1956 to describe collective electronic oscillations in solids which were very similar to electronic oscillations/surface waves in a plasma discharge (effectively the same formulae can be used to describe the frequencies of these physical phenomena). Surface waves originating in a plasma were initially considered to be just a tool for basic research, until they were successfully used for the generation of large-area plasmas for nanoscale materials synthesis and processing. To demonstrate the synergies between ‘plasmons’ and ‘plasmas’, these large-area plasmas can be used to make plasmonic nanostructures which functionally enhance a range of emerging devices. The incorporation of plasma- fabricated metal-based nanostructures into plasmonic devices is the missing link needed to bridge not only surface waves from traditional plasma physics and surface plasmons from optics, but also, more topically, macroscopic gaseous and nanoscale metal plasmas. This article first presents a brief review of surface waves and surface plasmons, then describe how these areas of research may be linked through Plasma Nanoscience showing, by closely looking at the essential physics as well as current and future applications, how everything old, is new, once again.

1 Introduction It is believed that a staggering 99% of the visible matter in the universe exists in a plasma state [3]. As shown 1.1 Opening remarks in Figure 1a, this spans 32 orders of magnitude from the very small plasmas in metals relevant in plasmonics around the order of a nanometre to massive extragalac- The recent explosion in nanoscale science and technology tic objects [4] (e.g., double radio galaxies) of the order of research has led to increased interest in the field of plas- 1023 m. Figure 1b narrows the focus to the types of terres- monics. With the wealth of exotic and exciting nanoplas- trial plasmas that are typically only found in a laboratory monic applications [1] that are now possible with the setting, demonstrating the relationship between gaseous unparalleled level of control over nanostructure growth plasmas and plasmonics through plasma nanoscience. In afforded by modern fabrication techniques it is easy to more detail, plasmonics (essentially plasmas in metals)is forget just how closely plasmonics is linked to traditional a way to exert a greater degree of control over photonics- plasma physics, both theoretically and experimentally. related applications i.e., confining and guiding light over Other comprehensive reviews have noted the important sub-wavelength scales through the use of nanostructures role played by plasma physics in the development and for- and thin films. Similarly, manipulating plasma resonance mulation of plasmonics [2]. However, the purpose of this sustained discharges is a way to exert control over nano- article is to present a discussion of how plasmonics and electronics by controlling the etching and growth parame- plasma physics are linked, not only via their theoretical ters of the nanoscale components (such as nanostructures and physical origins, but also through modern nanofabri- and thin films). The common link between all of these cation techniques – with a particular emphasis on plasma- fields is plasma nanoscience. Hence, as a result of the aided nanoscale synthesis and processing. This current nanoscale control over energy and matter that is possi- link will be demonstrated with a focus on the idea of res- ble in plasma nanoscience [5] (i.e. manipulating gaseous onances – e.g., gaseous plasmas sustained by resonances plasmas to create controlled nanoarrays), a clear link may will be linked to resonances of localised surface plasmons be drawn between gaseous plasma physics and photonics. sustained in and around solids. Moreover, it will be shown that the nature of collective a e-mail: [email protected] phenomena can mathematically be scaled up and down as Page 2 of 19 Eur. Phys. J. D (2012) 66: 226

Fig. 1. (a) Typical sizes of plasmas – from extragalactic plasmas [4] to the metal plasmas of our interest. (b) Logic flowchart – from gaseous plasmas to nanoelectronics and photonics, where ne is the number density of electrons. long as it is a plasma – from astrophysical plasmas to local surface plasmon resonances in metallic nanostructures. The colloquium is organised as follows: for the rest of this Introduction we will provide some definitions, followed by a brief historical account of the most important milestones both in plasma physics and in plasmonics. Fig. 2. Comparative sketches of (a) Volume plasmon (after Section 2 will then present the physics of surface waves, Maier [11]); (b) surface Plasmon Polariton; (c) Localised sur- coming predominantly from a plasma physics perspective. face plasmon. (b) and (c) reproduced with permission from [8], This will be followed by a discussion of the physics of sur- copyright 2007 Annual reviews. face plasmons in Section 3 with an emphasis on optics. The two areas will be drawn together in Section 4 where the backward electromagnetic (EM) waves (due to charge dis- field of Plasma Nanoscience [6,7] will be used as a back- placements caused by an incoming plane EM wave) – lead- drop to discuss the ways in which plasmonics and plasma ing to the creation of an energy gap [2]. The energy of the physics intersect. plasmon is [9]: Ebulk = ωp, (1) ω H 1.2 Definitions where p is the plasma frequency, as derived by . Mott- Smith [2]: 2 Before we can launch into a historical background or de- 4πnee ωp = , (2) tailed treatment, given the multidisciplinary nature of me plasmonics and the range of differing terminology used, n e a few definitions are necessary: where e is the electron density, is the charge of an electron and me is the effective mass of an electron. The Plasmons are quasi-particles that are collective oscilla- dispersion relation of a transverse volume plasmon is [2] tions of conduction electrons in a material, excited by elec- ω2 ω2 c2k2, tromagnetic radiation [8]. They are also referred to as a = p + (3) ‘quantized plasma (charge density) wave’ [9]. These oscil- k c lations are similar to the electronic plasma oscillations in where is the wavenumber and is the speed of light. a gaseous discharge, which led to Pines coining the term Hence, the phase and group velocities are given by: “plasmon” to describe the phenomena in 1956 [10]. Three v ω2 c2k2/k, types of plasmons are commonly referred to in the litera- ph = p + (4) ture: and Volume or Bulk plasmons are the cases discussed by 2 2 2 2 vg = c k/ ω + c k , (5) Pines and Bohm [12–14], visualised in Figure 2. Here, a p ‘bulk plasmon’ is the result of the creation of forward and respectively. Eur. Phys. J. D (2012) 66: 226 Page 3 of 19

Surface plasmon polaritons (SPPs) also referred to nanofabrication of metallic or doped semiconductor nano- as ‘propagating surface plasmons’ are a quantum of a po- materials which when excited by EM radiation at a specific larised EM wave (called a polariton) in a propagating frequency give rise to their own characteristic resonance medium coupled with a plasmon [9] – depicted in Fig- frequencies which can be used in various devices, e.g., sen- ure 2b. Assuming a perfect Drude free-electron model for sors, solar cells, etc. (see Fig. 1b). the dielectric function, the energy of a SPP in a thin metal film in air is [9]: √ 1.3 Historical background ESPP = ωp/ 2, (6) A comparison of the evolution of the plasma physics and where ωp is defined as in equation (2). Following on, the optics fields, with particular plasmonic milestones marked, characteristic SPP frequency is [11]: is presented in the timeline in Figure 3. Whilst the use of ω plasmons can be traced back to the 4th century AD (i.e., ω = √ p , (7) the Lycurgus cup, popularly in medieval stained glass win- sp ε 1+ 2 dows thereafter), with further commentary by Faraday in 1857 [17], an understanding of what they are and how they where ε2 is the real dielectric constant of the non- absorbing dielectric half-space in a typical SPP set-up [11] worked was not truly established until the 20th century. which will be described in more detail in Section 1.3. The basis for treatment of light scattering by metals was largely set by the end of the first decade of the 1900’s, Localised surface plasmons (LSPs) arise when light with seminal works including Drude’s treatment of metals hits a metal nanostructure. The light wavelength is much in 1900 [18] and Mie’s theory for scattering and absorp- larger than the nanostructure, leading to a plasmon os- tion of electromagnetic radiation by a sphere in 1908 [19]. cillating around the nanostructure [8] as depicted in Fig- These works still form the theoretical background of the ure 2c. The energy of a surface plasmon in a small metallic majority of papers on localised surface plasmons. sphere in air (again assuming Drude’s model for the di- On the other hand, while terrestrial gas plasmas (e.g. electric function) is [9]: lightning) has existed since primordial earth, experimen- √ tal studies on the fourth state of matter did not occur ELSP = ωp/ 3. (8) until 1879 by Crookes, with its more common name − plasma being coined by Langmuir in 1928 [31]. Langmuir Note√ a clear difference√ from equation (6), namely the use and Tonks followed this up with the observation of elec- of 3asopposedto 2. This is due to the effects of tron plasma oscillations (also referred to as Langmuir os- localisation (specifically, geometric confinement). cillations) in 1929 [35]. The earliest work on plasma res- A surface wave plasma is “a bounded plasma” which onance sustained discharges [36]isthatofTonks[32,37] “may support such (EM) waves which are guided along who derived the resonance frequency of a plasma (in a the boundary structure, their energy flux being concen- cylindrical discharge tube) in 1931 [37]: trated in the vicinity of this surface” [15]. In short, the √ ω ω / , plasma guides the waves, which in turn provide energy to = p 2 (9) sustain the plasma. Simply, this is a type of plasma that where ω is defined as in equation (2). is sustained by evanescently decaying electromagnetic sur- p The works of Zenneck [29] and Sommerfeld [30]from face waves, typically provided via a wave launcher such as 1899–1909 on electromagnetic surface waves can be re- a surfatron, surfaguide or microwave slot exciter/coupler. garded as one of the first linkages between plasmas and Initially, such plasmas were only possible in long, nar- plasmons, although neither were referred to as such at the row tubes – which made them useful as a diagnostic time. These Sommerfeld-Zenneck waves (SZW) are sim- tool, rather than a viable processing tool. However, re- ilar to SPPs, the difference that being the condition for cent developments have seen the generation of surface SZW is ε (ω) |ε (ω)| (where ε and ε are the imagi- wave plasmas larger than 1 m2 (supported by a dielectric i r i r nary and real parts of the dielectric function, respectively), plate, rather than a tube), which makes them particularly whereas for SPPs it is ε (ω) |ε (ω)| [38], i.e., ε must promising for large-area processing. i r r be of different signs for the two media for SPP, which is Resonances are a phenomenon that are intrinsic to a not the case for SZW. However, despite this, both fields bounded system. First discussed in the early 17th cen- existed separately for a long time with their common link- tury by Galileo in conjunction with his work on pen- ages not becoming clear until 1956 and 1957, first through dulums presented in Dialogues concerning two sciences, the work of Pines [10] and then Ritchie [28], who defined they can be simply thought of as sympathetic vibrations plasmons (in general) and surface plasmons (specifically), or defined in more detail as “an enhancement of the re- respectively. sponse of a system to an external excitation at a partic- The defining paper on Fano resonances [39] was pub- ular frequency”[16]. The idea of resonances is one that lished in Physical Review in 1961, presenting a formula- is central to this colloquium and in demonstrating the tion for the asymmetrical resonance peaks observed in the link between plasma physics and plasmonics. For exam- absorption profiles of Rydberg spectral atomic lines [16]. ple, gaseous plasmas sustained by resonances as a means of Previously, resonances had been considered to be totally Page 4 of 19 Eur. Phys. J. D (2012) 66: 226

Fig. 3. Historical timeline including relevant milestones in the fields of optics [17–27] and plasma physics [6,10,12–14,28–34]– from 1857 to the present day, discussed in detail in Section 1.3 of the main text. symmetrical peaks, i.e., Lorentzian [40]. Fano resonances The theme of sensing is of particular importance to have been used in local surface plasmon resonance (LSPR) plasmonics – not only through plasmon resonance spec- sensors [40]andwillbediscussedinmoredetailinSec- troscopy, but also via Surface Enhanced Raman Scatter- tion 4.3. ing (SERS). The SERS phenomenon was first observed by Other relevant breakthroughs in the area include the Fleischman et al. [22] in 1974 and explained in 1977 as re- development of the Otto [21] and Kretschmann configu- sulting from an electromagnetic enhancement mechanism rations for the excitation of SPPs [20], the latter being by Jeanmaire and Van Duyne [24] and as due to a chemi- the first experimental realisation of Sommerfelds surface cal enhancement mechanism (charge transfer) by Albrecht waves with visible light; both configurations debuting in and Creighton [23] − also in 1977. Both theories persist 1968. The difference between the configurations is that the to this day, appearing to be complementary, rather than Otto set-up has an air gap between the metal film and the exclusive interpretations of the SERS phenomena. prism (see Fig. 4d),aswellasathickermetalfilm(∼100’s Debate about the origin of the SERS effect, how- of nm vs. ∼ 50 nm for the Kretschmann configuration). ever, is still ongoing. Surface enhanced Raman-based The Kretschmann configuration (see Fig. 4e) is still being sensors employ a rough metal surface as a SERS sub- used in modern surface plasmon resonance sensing exper- strate. Typical examples include roughened noble metal iments. The Kretschmann angle, θ is the angle at which K films (e.g., Ag was used by Fleischman et al. [22]) and SPPs can be excited [41] and is defined via: more recently, nanostructured surfaces such as nanopar- √ ε ε ticle/nanodisk/nanotriangle arrays, etc. When the metal ε sin θ = m 2 , (10) 1 K ε + ε nanostructures are irradiated by a laser, which is in res- m 2 onance with the characteristic frequency of the material where ε1 and ε2 are the permitivities of the glass prism (i.e., 633 nm for bulk Au), plasmons are generated around and the medium in the half plane above the metal film, the nanostructure, which give rise to a significant enhance- respectively, and εm is the permittivity of the metal film ment in the local electric field around the nanostructure, in Kretschmann configuration. which in turn amplifies the Raman modes of the molecule Eur. Phys. J. D (2012) 66: 226 Page 5 of 19

Fig. 4. (a) Surface wave tubular discharges, reproduced with permission from [44], IOP Publishing Ltd.; (b) generation of linear surface wave discharge and relation of number density to resonance, reproduced with permission from [45], IOP Publishing Ltd.; (c) reactor schematic for production of large area surface wave plasmas, reproduced with permission from [46], IOP Publishing Ltd., (d) Otto configuration for excitation of surface plasma waves – from [47], Copyright 1997 The Japan Society of Applied Physics. (e) Kretschmann configuration for excitation of SPPs used in SPR, reprinted from [48], with permission from Elsevier. being studied. Hence, it may be recognised that SERS is Rhodamine 6G of the order of up to 1014–1015 [26]. These in essence, due to its reliance on plasmons, a plasma effect. marked enhancements are of great interest as it makes the An expression for the SERS enhancement factor is detection of ultra low concentrations of molecules (per- given by [8]: haps even single molecules) of biomedical and other inter- ests possible. [ISERS (ων )/Nsurf ] EFSERS (ων )= , (11) Ebbessen et al. in 1998 [27] demonstrated ‘extraor- [INRS (ων )/Nvol ] dinary optical transmission through sub-wavelength hole arrays’. This was due to optical coupling of incident light where ISERS is the intensity of the SERS signal, INRS with plasmons from sub-wavelength hole arrays in Ag is the intensity of the normal Raman signal, Nsurf is the number of molecules bound to the SERS substrate and films. This use of SPPs is particularly promising for optical waveguides. Nvol is the number of molecules in the excitation vol- Other more recent milestones in the plasma physics ume [8]. The intensity of the SERS signal, ISERS can field include the discovery of carbon nanotubes in an arc be expressed as M(ωL)M(ωR)INRS [42], where M(ω)is the field intensity enhancement due to plasmon resonances discharge in 1991 by Ijima – this is a notable linkage be- and ω and ω are the exciting laser frequency and emit- tween plasma physics and nanoscience. This increasing L R convergence of the plasma physics field with the emerging ted photon frequency, respectively [42]. Hence, ISERS can be regarded as due to a plasma effect of plasmon reso- micro- (and then nano-) technology disciplines led to the nance. formation of the Plasma Nanoscience research field, the An extension is single-molecule SERS sensors [43] main principles of which were formulated fairly recently which harnesses plasmonic hot spots (resulting from cou- and will be discussed in greater detail in Section 4. pling between individual nanostructures) to detect ultra low concentrations of molecules. Single molecule SERS was first observed in 1997 through the work of Nie and 2 Plasmons for Plasma physics: the physics Emery [26]. This phenomenon occurs when plasmonic of surface waves nanostructures are brought within a certain distance of each other resulting in the creation of ‘hot spots’ (first 2.1 General characteristics of surface wave discharges studied by Stockman et al. [25] in 1996), which are areas of intense electromagnetic field strength – leading to ex- As noted in the introduction, surface wave plasma (SWP) tremely large SERS enhancement factors, in the case of resonance sustained discharges [49] have been investigated Page 6 of 19 Eur. Phys. J. D (2012) 66: 226 for a number of decades, first as a promising diagnostic caying EM surface waves propagating along a discharge tool (e.g., elemental and spectral analysis [49]) and more tube [58,59], an example is shown in Figure 4a. A typi- recently as high-density, large-area plasma sources [46]. cal set-up is shown in Figure 4b[45,46]. Figure 4bshows The use of surface waves in large-area processing has seen a standard linear/column set up, with a SW launcher them move from an object of purely academic research (i.e., surfatron/surfaguide) and a dielectric tube which the to a viable fabrication route. More interesting is the idea plasma is contained in. Such plasmas are of limited volume that the physics of surface waves (SW) is easily extended and are not uniform – a clear disadvantage for materi- to the physics of surface plasmons. Moreover, these classi- als processing [45]. Simple tweaks are possible to improve cal expressions can be fairly easily extended to deal with performance, i.e., axial non-uniformity can be avoided by phenomena that can be regarded as quantum in nature. placing a wave launcher at each end of plasma tube, which This will be discussed in more detail in Section 3.3. causes the wave to be reflected at the end of the tube [15] Suffice to say, for our purposes the main things we need (this can also result in a standing SWP [60]). to know in general about SWPs is that [15]: The dispersion relation for a TM propagating surface – The discharge can be sustained far away from the wave is [61]: launcher. ω2 ω2/ c2k2 − ω2/ c4k4 1/2, – A broad range of excitation frequencies may be used = p 2+ ( p 4+ ) (12) (i.e., from 10 MHz to 10 GHz – however, the most where c is the speed of light and k is the wavenumber. common frequencies used are 2.45 GHz or 915 MHz). Essentially these SWs propagating along a dielectric On that note, it should be mentioned that the choice of tube are macroscopic microwave analogues of the surface the frequency of the power source is determined by the de- plasmon polaritons discussed in Section 1.2. sired plasma density (to meet the resonance frequency in any particular geometry and reactorsize)whichinturn is controlled by the pressure, feedstock gas and amount 2.3 Plasmas sustained by standing surface waves of power we can couple to the discharge. Since, typically a dense plasma of ≥1011 cm−3 is sought after (for semi- Figure 4c shows a planar surface wave plasma source [62], conductor production the plasma must be dense), then a where instead of a dielectric tube, the plasma is sustained matching GHz excitation frequency should be used. Sim- below a dielectric plate. There are numerous variations on ilarly, in plasmonics, it is the available number density of these planar designs, leading to improved densities, homo- electrons in a low-loss metal that determines the choice geneity, etc. We refer the interested reader to a number of of the frequency of the EM radiation (for example, the articles for a thorough examination of the various source wavelength of a laser). These parallels will be discussed in configurations [15,45,50,55,63–68]. In this case, it is the greater detail in Section 3.3. plasma sustained by standing SWs that is of interest. Other salient features of SWPs include [15]: The dispersion equation for a standing transverse magnetic surface mode (TMmns )is[64]: – The gas pressure range used is quite large – i.e., from sub-mTorr under electron cyclotron resonance (ECR), (γd/εd) tanh(γddth)=γp/εp, (13) to a few atmospheres. Subsequently, there is a large range for the plasma density [15]. where γd and γp are the inverses of the penetration depths – Given the recent design modifications, use of SWPs (where γ = −(κ2 − εω2/c2)1/2 [64]) in a dielectric window is quite flexible and energy efficient for a variety of and plasma, respectively and dth is the thickness of the applications. dielectric layer. – SWPs are extensively modelled [15,50–54] (and hence The frequency of resonance may be obtained from [55]: well understood). −1 – Regarding the surface wave modes that sustain SW ω2 4 2 p ω βd ω discharges, the notation is as follows TMmns ,where =1± + tan2(β d ) − ω2 c2κ2 ε κ2 d dp c2κ2 m, n and s are the azimuthal, radial and axial indices, 4 dp 2 respectively and TM refers to a transverse magnetic (14) wave (similarly TE is a transverse electrical wave) [55]. where εdp and ddp are the permittivity and thickness of the dielectric plate, the transverse wave number is κ = Umn/R In addition to thinking of these plasmas as linear sur- U n m face wave discharges or planar surface wave discharges, where mn is the th root of the order Bessel function and R is the chamber radius, whereas the axial wavenum- we can also categorize SWs as propagating (see Sect. 2.2) 2 2 2 ber is βd = εdpω /c − κ . For pure surface modes, or standing (see Sect. 2.3) and the plasmas as plasmas s produced by the propagating and standing surface waves, = 0. Essentially these TMmns (via a large dielectric respectively. plate) are big microwave analogues of localised surface plasmons from the optical range. Examples of discrete, pure surface modes [46] in the microwave frequency range 2.2 Plasmas sustained by propagating surface waves of our interest are: TM53,TM62,andTM33. For more details about current efforts in modelling a AsnotedinSection1.2,asurfacewavesustaineddis- range of SW discharges (both planar and tubular) we re- charge [56,57] is a plasma generated by evanescently de- fer the interested reader elsewhere [69]. Further relevant Eur. Phys. J. D (2012) 66: 226 Page 7 of 19

Table 1. Relevant equations and parameters for comparison of surface wave plasmons and surface wave plasmas. Symbols are deﬁned as in the main text, Table 2 or as follows: nc is carrier concentration and w is the width of a graphene micro-ribbon [143].

−3 No. Name λ or freq. Dispersion equation ne [cm ] Freq. of resonance References √ ω2 ω2/ c2k2 ≥ 11 ω ω / ε 1SWTMMHz–MW = p 2+ 10 SW = p 1+ d equation (12), − ω2/ c4k4 1/2 mode ( p 4+ ) [61] (travelling) 11 12 2SWTMMW(γd/εd) tanh(γddth)= 10 –10 equation (14)[55,64] mode γp/εp (standing) ω2 ω2 c2k2 22 ω 3 Bulk plasmon NIR, Vis, = p + (trans) 10 p [9] UV √ ω2 ω2/ c2k2 22 ω / 4 SPPs NIR, Vis, = p 2+ 10 p 2[219] − ω2/ c4k4 1/2 UV ( p 4+ ) 22 23 5 LSPs NIR, Vis, geometry dependent 10 –10 (Au, when εr(ω) ≈ [78] UV Ag, Cu, etc.) −2εmed (metal) ω2 ω2 e2|qz¯ 0 16 19 ω ∝ n1/4w−1/2 6 Plasmons- THz, NIR = 2D(1 + 10 –10 p c [143–147,164,220,221] ω2/ ω2 − ω2 graphene ( p (2 p))) equations and parameters for SWPs including the res- The extinction and scattering cross sections arising onant frequency, dispersion relation etc. are listed in from Mie’s solutions to Maxwell’s equations (when the Table 1 in Section 3.3. particle is much less than wavelength, λ)are[72]:

Current research: Recent developments in antenna de- 3/2 . × . 2 18πεmedV εi(λ) sign have led to the production of a 1 3 1 1m sur- σext , = 2 2 (16) face wave sustained plasma at 915 MHz, with uniform λ [εr(λ)+2εmed] + εi(λ) plasma of ∼2.7 × 1011 cm−3 (electron number density, 4 2 2 2 2 ∼ 32π εmedV (εr − εmed) +(εi) standard deviation 5%, operating pressure 10 Pa) [66]. σscat , = 4 2 2 (17) Such large-area plasmas are of great promise for the mi- λ (εr +2εmed) +(εi) croelectronics and photovoltaics industries, in particular for the production of large liquid crystal displays and so- where V is the volume of the particle,ε ˜ = εr + iεi is the ε n2 − n2 lar cells. Plasmas, in general, have been used to process Si complex metal dielectric function, where r = r i 2 panels approaching 4 m [70]. and εi =2nrni are the real and imaginary parts ofε ˜ and nr and ni are the real and imaginary parts of the ε n2 complex refractive index of the metal, and med = m is 3 Plasmons for photonics: the physics the dielectric function of the medium [72]. Generalisations of these equations for spherical parti- of surface plasmons cles of any other aspect ratio is possible via Rayleigh-Gans theory [9,73,74] (for a more detailed coverage, please refer 3.1 Physical foundations for surface plasmons to Bohren and Huffman [9]). For other shapes, however, analytical solutions are not available [72]andtheymustbe The physical foundations for surface plasmons consist of studied numerically or via plasmon hybridization theory. a few major milestones including, but not limited to: Mie The advent of plasmon hybridisation theory [75] in 2003 theory [19] for absorption and scattering of light by spheri- has made it easier to analytically describe plasmon modes cal particles and the Drude free electron model for metals in a range of exotic nanostructures, from nanoshells [75], etc. [18]. The Drude model assuming free electrons in a to nanorice [76], to nanotubes with dielectric cores [77]. metal is given by [71]: This is done by describing the interaction of plasmon modes supported by basic structures. For example, plas- ω2 mon modes of nanoshells could be described as two fun- ε(ω)=1− p , (15) ω2 damental dipolar modes [11], with one mode supported on the outside of a larger outer nanosphere and one mode where ωp is the plasma frequency, defined in equation (2). on the surface of a smaller inner dielectric nanosphere or It should be noted that Mie theory, by itself, is geometric – ‘void’ [77]. Some further important relations, i.e., disper- the effect of a plasma is taken into account when the Drude sion equations and resonant frequencies of SPPs and LSPs model is used to describe the dielectric function of the are listed in Table 1 and discussed in greater detail in metal (see Sect. 4.4 foranexpandeddiscussion). Section 3.3. Page 8 of 19 Eur. Phys. J. D (2012) 66: 226

Table 2. List of symbols and abbreviations from manuscript Quickly revisiting equations (16)and(17), for a single and their meanings, the equation and/or first section they are nanoparticle (NP), Mie theory has the extinction (sum of mentioned in. absorption and scattering cross sections) as [78]: Symbol Meaning Eq. or Section εi ωp Plasma frequency 2 E(λ) ∝ , (18) ε χε 2 ε Ebulk Energy of a bulk/volume 1 ( r + med) + i plasmon χ SPP Surface Plasmon Polariton Section 1.2 where is a form factor related to the nanoparticle’s as- ESPP Energy of a surface plasmon 6 pectratio(2forasphere)[78]. Local surface plasmon polariton resonance occurs at the maximum of the right hand side ε ω ≈−ε ωsp SPP frequency 7 of equation (18), which is where r( ) 2 med (when LSP Local Surface Plasmons Section 1.2 |εr|εi)[78]. It should be noted that classical Mie the- ELSP Energy of a local surface plasmon 8 ory (unmodified) is not appropriate for interacting nanos- ne the electron density 2 tructures (this is particularly important to note when de- e the charge of an electron 2 signing arrays intended to take advantage of plasmonic me the rest mass of an electron 2 effects). vph phase velocity of transverse bulk 4 plasmon vg group velocity of transverse bulk 5 3.2 Materials design for surface plasmons plasmon c speed of light 5 When thinking about what type of nanostructure to grow, λ wavelength 16,17 one must have a very specific application in mind. This k wavenumber 5 ε˜ complex metal dielectric 16, 17 is because the size, shape, composition, spacing etc will function affect how the nanostructure reacts. The number of free

εi imaginary part ofε ˜ 16, 17 carriers determines the performance of the plasmonic ma-

εr real part ofε ˜ 16, 17 terial. For example, something as simple as composition – εmed dielectric function of the medium 16, 17 a 633 nm laser will excite Au whereas 532 nm is more ap- σext extinction cross section 16 propriate for Ag. What also must be considered – is the σscat scattering cross section 17 price of the material, worth the application? For exam- V volume of the nanoparticle 16,17 ple, is a better plasmonic quality factor worth extra cost? n refractive index Section 3 Note that the plasmonic quality factor varies for diﬀerent QLSPR quality factor of plasmonic 19 geometries and for metals it is [79]: material for LSPR-spherical 2 QLSPR quality factor of plasmonic 19 ε (ω) ε (ω) QLSPR(ω)=− ,Q (ω)= , (19) material for LSPR-ellipsoidal ε(ω) LSPR ε(ω) E(λ) LSPR extinction 18 χ form factor for nanoparticle 18 where QLSPR is for spheres and QLSPR is for ellip- aspect ratio soids [79]. θK Kretschmann angle 10 Sodium and Potassium have higher quality factors – ε1 permittivity of a glass hemisphere, 10 for excitation of SPPs in Kretschmann but they are so volatile that they cannot be practically conﬁguration used by themselves (imagine if Potassium came into con-

εm permittivity of metal film in 10 tact with water – then consider that a lot of the biospecies Kretschmann configuration that have to be analysed using LSPR may be in aqueous ε2 permittivity of medium in upper 10 solution.). Silver, for example has a higher Q than Au, half plane above metal film in however it is toxic – so therefore not appropriate for some Kretschmann configuration bio-related applications [80]. Clearly there are a lot of fac- Δλmax Maximum λ shift on adsorption 21 tors to consider – having the best performing material is of a biospecies not always the way to go, it is more like having the best fit nbulk bulk refractive index of 21 material for a number of considerations both performance nanoparticle Δn Change in n caused by adsorbate 21 (high quality factor) and practicality (ease of fabrication, d adsorbate layer thickness 21 excitation in the visible range of the EM spectrum, i.e., white light), in other words – the choice of material is a ld EM field decay length 21 SERS Surface Enhanced Raman Section 1.3 balancing act. The optical properties of Ag and Au in the Scattering visible range can be described viaε ˜, the complex metal EFSERS SERS enhancement factor 11 dielectric constant [78]. Nevertheless, the electron density, ISERS Intensity of SERS signal 11 which determines the frequency of plasma resonance still INRS Intensity of Raman signal 11 remains the main factor in the material choice. Nsurf number of molecules bound to 11 Whilst the ‘coinage’ metals (Au and Ag) possess ac- SERS substrate ceptable plasmonic merit, the reason they are more widely Nvol number of molecules in the 11 used than other materials which may have a greater num- excitation volume ber of free carriers (i.e., Alkali metals such as Na and K) Eur. Phys. J. D (2012) 66: 226 Page 9 of 19 is due to their relative inertness and experimental con- the number of which depends on the number of ways the venience (i.e. they are more convenient than the Alkali shape can be polarised [78,80]. For example, for metal- metals whose volatility makes them difficult to use) [81]. lic nanorods, two plasmon modes are present, namely a In fact it is well recognised that both of these materials longitudinal mode (polarisation parallel to the long axis, are quite lossy, that is the signal carried on these materials red shifted) and a transverse mode (polarisation perpen- degrades very rapidly (not a huge issue for sensing, but a dicular to the long axis, blue shifted) [78]. Here we stress big problem for application in an ‘all optical chip’). This that quite similar polarisation effect happen in (gaseous) has led researchers to consider using alternative, combi- plasma waveguides which determine their eigenmodes [56]. natorial materials such as doped metals, alloys or inter- As well as size and shape, tailoring the spacing between metallic compounds, all of which enable a greater degree nanostructures is another way to control the plasmonic of flexibility when attempting to tune the plasmon reso- response of the array. For example, Jain et al. [93] derived nance [81–86] which is one of the drawbacks in just using the ‘plasmon ruler’ equation as: pure Au or Ag. As yet, the barrier to widespread imple- mentation of these intermetallic compounds or alloys for Δλ −s/D ≈ 0.18 exp , (20) plasmonic applications is the lack of carefully designed, λ0 0.23 commercially viable fabrication methods with a high degree of control over size, shape, composition and place- where Δλ/λ0 is the observed plasmon shift, s is the in- ment of plasmonic nanoparticles. terparticle edge-edge separation and D is the particle di- Hence a checklist to consider when choosing the mate- ameter – for a pair of Au particles in a protein medium. rial to use for plasmonic nanostructures is: Depending on how close the nanostructures are to each – Does it have a matching electron density? other, their surface plasmons may constructively interfere – Does it have low losses? and result in a marked enhancement in the local electric – Does it have an acceptable Quality factor? field. This is particularly important in the case of ‘hot – Is it convenient to use/produce? spot’ generation. Hot spots [25] are the term given to ar- – How to fabricate it, including nanoarrays? eas of intense electric field enhancement [41,94–96]. These – Is it robust/relatively inert? areas are particularly useful for single molecule sensing 14 – Can it be integrated into existing technology? (and can often lead to SERS enhancements of up to 10 ). – Does it work in the visible range of the EM spectrum? However, controlling (or even predicting) where hot spots – Is it comparatively cheap? will occur is very challenging. This means particular atten- tion (and thorough modelling efforts) need to be directed Surface plasmons are very sensitive to their local sur- at understanding and finding fabrication methods capable roundings, leading to a wavelength shift, a change in an- of controlling the coupling between plasmonic nanostruc- gular momentum or a change in intensity if there is a tures with various sizes, shapes, composition, spacing and modification in the local refractive index. These charac- orientations [91,97–107]. The tailoring of NP size, shapes teristics are detectable and may be used to great effect in and array properties such as ordering, regularity etc. is sensors. As well as sensors, LSPs are useful for solar cells, what is commonly pursued in Plasma Nanoscience and optical computing and biomedical applications (including will be discussed in greater detail in Section 4. cancer treatment) [87]. For smaller nanostructures (radius <∼ 30 nm), absorption dominates LSPR extinction, whereas scatter- 3.3 Comparison of plasmas and plasmons ing dominates for larger nanostructures (radius >∼ 30 nm) [80] – consider equations (16)and(17) (this is one of the reasons that larger Ag nanostructures are promis- Let us now summarise the collective phenomena discussed ing for plasmon enhanced solar cells (and LEDs) – the in Sections 2 and 3, through comparison of their main scattering is enhanced leading to an enhancement in the equations and features as presented in Table 1. solar cell efficiency [88–90]). Regarding shape [91,92]–it Just looking at the energies of the oscillations confirms is documented that there is higher refractive index sensi- the common ground – i.e.√ compare the energy derived from E ω / E tivity for higher aspect ratios i.e., 157–497 nm/RIU from equation (9): = p 2, which is identical√ to√ SPP√ aspect ratio of 1.0 (sphere) to 3.4 (nanorods, described by (Eq. (6)) and only differs by a factor of 1/ 2and 3/ 2 spheroidal model) [72], where RIU is refractive index unit. for Ebulk (Eq. (1)) and ELSP (Eq. (8)). However, it is not Moreover, nanostructures featuring sharper tips also ex- just an issue of energies and resonant frequencies, the syn- hibit enhanced sensitivity to changes in their immediate ergism of the plasma physical phenomena and plasmonic surrounding environment [72]. This may also be linked to physical phenomena follows from this table. hot spot enhancements around the tips of nanostructures For example, compare the dispersions relations of sur- due to the so-called “lightning rod effect” [11]. For the face plasmons (Row 4) and TM surface plasma modes – cases where nanostructures are non-spherical, the number travelling (Rows 1) – the form is exactly the same in gas of resonances increases as the facets increase, e.g., a cube plasma and metal plasma (the dispersion relation in (1) has more plasmon resonances than a triangle, which has is the same as the dispersion relation in (4), despite there more than a sphere [80]. In other words, if the structure being about a 1011 cm−3 difference in electron number is ‘anisotropic’ it can support multiple plasmon modes, density. In particular, as noted in Sections 2.2–2.3 the TM Page 10 of 19 Eur. Phys. J. D (2012) 66: 226 modes in a SWP via a dielectric tube and a SWP via a di- ‘knobs’ such as gas inlet, pressure, partial pressure of the electric plate are analogous to surface plasmon polaritons gases, applied power, applied voltage, degree of ionisa- and localised surface plasmons, respectively. tion, etc. These knobs can be manipulated, resulting in an efficient growth process. Secondly, in order for plasmonic devices to be widely adopted, they must be able 4 Everything old is new again: plasma to be easily integrated into existing semiconductor-based nanoscience meets plasmonics devices. Wet chemical production methods are not easily integrated into existing manufacturing lines. In con- 4.1 Introduction to plasma nanoscience trast, over 50% of semiconductor manufacturing lines are plasma-based [116]. This means that by using plasmas as Plasma nanoscience [108–112] is a research field which a fabrication basis, existing production lines could be used incorporates elements of plasma physics, nanoscience, ma- to make plasmonic nanostructures that could be easily in- terials science and engineering, physical chemistry and tegrated into current devices, improving their performance surface science, that is centered on elucidating how a and efficiency (both in terms of energy and matter [108]), plasma-based growth environment may be used to bring without the need for a costly, full-scale overhaul of produc- self organisation of nanostructures up to the as yet elu- tion lines. Moreover, a plasma-based fabrication method sive, deterministic level [6,7,34,110,113,114]. A determin- is capable of large-area (and large volume) processing – istic fabrication process is one where it can be predicted as noted above 1.3 × 1.1m2 surface wave plasmas have with a great degree of certainty what type of nanostruc- recently been achieved [66]. ture will be produced, from what type and how material is deposited on a surface. This idea of determinism is particularly important for the fabrication of nanoarrays for 4.2 Tailoring metal nanoarrays plasmonic applications where control of size, shape, elemental composition and positioning is crucial. Finding In order to optimize the sensitivity and performance of a growth/processing environment that is capable of pre- plasmonic based devices, it is necessary to precisely tailor cisely ‘tuning’ these parameters is a significant challenge. the nanoarray parameters as noted in Section 3.Themost Low-temperature, non-equilibrium plasmas are a particu- significant parameters to control include: nanostructure larly versatile tool for this purpose [6]andmaybeusedfor size, shape and composition as well as nanoarray spacing all stages of the growth process from generation of build- and surface coverages. ing and working units in the plasma bulk (building units For the majority of modern technological devices, a are the material that make up the nanostructure, work- regular array of uniform components is required [117]. ing units prepare the surface for deposition), through to This is because the coupling between nanostructures in surface preparation, directed transport of materials to the thearraymustbeabletobecontrolledtotailorthe surface, nanoassembly of highly-tailored structures as well optoelectronic properties of the device. However, there as functionalisation and post-processing of arrays. A re- are a few obstacles in obtaining size-uniform nanostruc- view by Anders [115] highlighted the use of plasmas of tures with high throughput and at a low cost. Plasma- metal vapours for production of metal nanostructures. An based growth methods [115,118–120] have been shown interesting point to note is that these plasmas of metal to be promising controllable bottom-up alternatives for vapours can be tailored to produce metal plasmas (i.e., size-uniform and size-controlled growth. For example, collective electron oscillations with respect to the positive it was demonstrated numerically [118,119]thatplas- ion background in the metal nanoparticles from the con- mas lead to a greater degree of nanostructure size uni- densing of the metal vapour). formity than is possible in a neutral gas-based self- As noted previously [113], a range of factors need to be organized process. Highly-ordered nanostructure arrays considered when choosing a fabrication technique, some of have been reported (experimentally) using inductively these factors include: coupled plasmas (ICPs) [121], atmospheric microwave plasma torches [122], single-step deep-reactive-ion etch- – Process control. ing [123] and a range of other plasma-based techniques. – Energy efficiency of the fabrication process. This is particularly important for nanoplasmonics as con- – Quality of the material output. trolling the coupling between nanostructures by varying – Integration with existing technology. size and position is a way to fabricate devices which can – High throughput. take advantage of plasmonic effects. – Large area and volume processing. Regarding controlled shapes, plasma-based growth – Simplicity – i.e. is it easy to use? methods have been used to grow a large variety of nanos- – Cost. tructures – from quantum dots, nanotips, graphene, even – Safety factors – i.e., is it human health benign? nanoarchitectures (i.e., Ag islands connected by carbon – Environmental impact. nanowires – the first steps to self-organised nanocircuitry In reference to this checklist-style approach, there are a growth [120]). Controlling nanostructure shape is partic- number of reasons for choosing a plasma as a nanofabri- ularly important in plasmonic applications, as mentioned cation environment over other techniques. Firstly, plasma- in Section 3. For example, it has been demonstrated that based systems offer a number of effective process control sharper tips and higher aspect ratios lead to the increased Eur. Phys. J. D (2012) 66: 226 Page 11 of 19 sensitivity to changes in the refractive index [72]. In- shown to exhibit plasmonic behaviour. Whilst graphene deed, plasma effects (i.e. resonance around the plasma and its derivatives [143–147] have been used in combi- frequency) will affect intra- and interparticle coupling de- nation with metallic nanostructures for plasmonic-based pending on the nanoparticle size, shape, and distance be- sensing [148], it is also useful by itself. In fact, a quasi- tween them. Recall from Sections 3.1 and 3.2,theLSP particle termed a ‘plasmaron’ (combination of a plasmon properties are determined by the plasma density and 3 and an electron) was recently observed in free stand- geometric factors (see Eqs. (16)and(17) for the influence ing graphene [149]. For graphene, plasmons are excited of size, Eq. (18)shapeandEq.(20) for distance). in the near infrared (or THz range) [150,151]. Koppens Low-temperature plasmas have been demonstrated to et al. [152] summarise the main advantage of graphene produce sharper carbon nanotips than is possible in a neu- plasmonics over traditional noble metal-based plasmon- tral gas process [124]. Moreover a recent review on the use ics as: tighter confinement, longer propagation distances of metal vapour plasmas for the growth of metal nanos- and high tunability. Moreover, they state that using tructures [115], noted that there were a number of options graphene, may pave the way towards ‘quantum plasmon- including ionised physical vapour deposition (iPVD) based ics’ [152]. The study of collective quantum effects in plas- on sputtering (more appropriate for Ag), as well as pulsed mas [153–163] and particularly in graphene [164–166]isa laser deposition, filtered cathodic arcs, etc. The benefit significant challenge that is likely to be the subject of in- of using plasma-enhanced magnetron sputtering is that it tense research efforts in the future. Plasmas have been is possible to exert a high level of control over both the shown to be a very promising way to make graphene- direction and the energy of the charged particles. Indeed, based structures, the particular benefit is that they may be both those factors are responsible for dislodging the metal grown without the presence of a metal catalyst [148,167]. atoms from the target, as well as ionising and then controlling the metal atoms themselves. This in turn affects the 4.3 Existing and emerging applications way particles self-organise into a nano-array. Whilst the most popular methods to form nanostructures for plas- As shown in Figure 5, there is a range of applications that monics are currently e-beam and nanosphere lithography work based on plasmonic phenomena. Moving clockwise and nanotemplating, plasmas are a useful alternative that from the top left hand corner, these include: a (proposed) can be used to control the deposition of metals or metal plasmon cloaking device [174,175], single-molecule SERS oxides through nanoporous templates to create size uni- sensing platforms that rely on plasmonic hot spots [169], form, regular arrays [125,126], as well as in conjunction theranostics [170], surface plasmon lasers or ‘spasers’ [173, with nanosphere lithography [127]. This control over the 176,177], LSPR biosensors using simple LEDs [172], next- generation of nanostructure material, transport to and generation photovoltaic cells [87] and plasmon rulers [171]. interaction with the surface is enabled by careful mod- This is of course a non-exhaustive list that is meant to just ification of the plasma parameters such as power, pres- give an idea of how many fields plasmonics is involved in. sure, gas composition, etc. as well as the external surface For the purposes of this section, we will focus mainly on bias [128–132]. photovoltaic cells, sensors (SERS, SPR and LSPR-based) Changing nanostructure size and shape, however, can and biomedical applications. be problematic in certain biological and nanoelectronic Photovoltaic cells can utilise plasmons by incorporation applications [116,133]. As mentioned in Section 3,anal- of nanoislands/nanostructures into bulk and thin-film Si ternative is to change elemental composition and internal solar cells. The key is to design the nanostructure geom- structure (i.e., core/shell layers, compositionally graded etry such that the enhanced forward scattering into the structures, etc.). This enables another possibility, namely photoactive layer obtained via coupling of surface plas- the composition control. Using more complex materials mons is not overshadowed by strong absorbance of inci- (i.e., binary and ternary alloys, etc.), however, brings the dent light at the plasmon resonance wavelength of the issue of control back. The growth process must be tai- nanoparticles [178]. Recall Section 3, in particular equa- lored so that materials may be grown not only with the tions (16)and(17) which showed that scattering domi- desired shape and size, but also the right composition and nates in larger particles whereas absorbance is more im- internal structure. This necessitates thorough modelling portant for smaller particles. By using relatively large efforts to determine exactly what fabrication method will Ag islands (around 50 nm) the scattering of light into result in structures with the size, composition, shape and the PV cell is enhanced, the plasmon resonance of these internal structure that will in turn generate the desired particles can be tuned so it is around the desired wave- plasmonic response. Gaseous plasmas represent an ideal length by modifying the surrounding local dielectric en- fabrication environment for this purpose. A high degree vironment [179]. Note that the enhancement may be op- of compositional control during nanoassembly has been timised by varying the shape, size, material and surface demonstrated for plasma-based processes both computa- coverage of the nanostructure [178–184]. Figure 6ashows tionally [113,116,134,135] and experimentally [136–141]. that higher aspect nanostructures (i.e., cylinders rather In addition to manipulating traditional plasmonic ma- than spheres) maximises the fraction of incident light scat- terials such as Au and Ag by alloying or doping, alterna- tered into the photoactive layer and hence enhances the tive materials such as graphenes, doped semiconductors, solar cell efficiency [180]. Akimov et al. numerically inves- carbon nanotubes [142] and multilayers have also been tigated the effect of the the size and surface coverages Page 12 of 19 Eur. Phys. J. D (2012) 66: 226

Fig. 5. (a) A plasmon ‘cloaking device’, reproduced with permission from [168], IOP Publishing Ltd; (b) a plasmonic ‘hot spot’, reprinted by permission from Macmillan Publishers Ltd: Nature [169], copyright 2011; (c) the various theranostic applications of plasmonic nanoshells, reprinted with permission from [170], copyright (2011) American Chemical Society. (d) Plasmon rulers, from [171], reprinted with permission from AAAS; (e) next generation photovoltaic cells, reprinted by permission from Macmillan Publishers Ltd: Nature Materials [1], copyright 2010; (f) and (g) LSPR biosensors using simple LEDs, reprinted with permission from [172], copyright (2008) American Chemical Society; (h) surface plasmon lasers or ‘spasers’, reprinted by permission from Macmillan Publishers Ltd: Nature [173], copyright 2009. of Ag nanoparticles [183,184] on light absorption in Si enhance the efficiencies of photovoltaic cells. A good re- thin film solar cells. They found that for Ag nanoparti- view on various configurations of metallic nanoparticles cles, there were 2 best configurations that would maximise and metallic films for the purpose of enhancing the ef- the forward light scattering and minimise absorption by ficiencies of solar cells was recently published by Green the nanoparticles in the wavelength range of interest, by and Pillai [187]. They note that when metallic films are optimizing the higher order plasmon modes and shifting attached to the rear surface of the photovoltaic cell, the the lower order resonance modes into a less important resultant SPPs can significantly enhance photovoltaic cell wavelength range. This effort was extended to investigate absorption. Moreover, the combination of a metallic film other materials as shown in Figures 6band6c. In another as a reflector at the back of the cell, combined with sand- paper [185] the enhancement due to resonant plasmonic wiched high index – low index – high index layers and a metals (Ag) was separated from the effect of non-resonant textured front surface has been shown to significantly en- plasmonic metals (Al). hance light trapping of the photovoltaic cell [187]. They Methods to construct nanostructure arrays suitable also note that the location of metallic nanostructures for this purpose include fragmentation after thermal (hence resultant LSPs) within or without the cell is im- evaporation [179], as well as plasma-assisted nanosphere portant – it has been suggested that the performance of lithography [127] and plasma-assisted deposition through the cell may be improved by placing metallic nanostruc- nanopore arrays [125,126] discussed in Section 4.2.The tures closer to the most active region of the cell, rather benefit there is that the size of the nanoparticles in than just on the top surface of the cell [187]. It is pos- template-based methods is more controllable than in sible that metallic films, hence SPPs may be used in a stress-induced fragmentation [186] which results in a very similar configuration for this purpose – Green and Pillai broad island size distribution. Given the rather large include a sketch of a proposed cell based on the work of size of the islands required, i.e. 50 nm, plasma-assisted Wang et al. [188] which consists of a indium tin oxide layer nanosphere lithography and nanopore templates are suit- (55 nm), the rear segment of which contains a 20 nm layer able – in the case where smaller islands are required (often of Ag which covers 54% of the cell; this is followed by a the case for sensor devices), a bottom-up growth route, 15 nm thick amorphous Si layer and then a 50 nm thick such as plasma-based self-organisation is more appropri- Ag layer as a rear reflector [187]. ate. Sensors based on plasmonics can function optically or In addition to metal nanoparticles and associated electronically. However, herewewillfocusonSPR,LSPR LSPs, metallic films and resultant SPPs may be used to and SERS-based sensors. Surface Plasmon Resonance Eur. Phys. J. D (2012) 66: 226 Page 13 of 19

where the bulk refractive index of the nanoparticle is nbulk , Δn is the change in refractive index caused by the adsorbate, d is the adsorbate layer thickness and ld is the EM-field decay length [8]. Neuzil and Reboud [172]con- structed a handheld, battery-operated LSPR-based sensor, where 4 light emitting diodes were used in place of a spectrum analyser (a schematic and image of the device are shown in Figs. 5fand5g). Such a device is particularly promising as a portable, point-of-care detection system – not the least because it is mechanically simpler than an SPR analogue (it is the change in wavelength that is important – not the change in angle of reflection) [172]. Additional refinements to LSPR spectroscopy lie in util- ising Fano resonances [16,40,198], the extreme sensitivity to changes in the local environment around the resonant structure suggest that detection of single molecule binding events may be possible [40]. This will likely be an area of intense research efforts in the near future. Surface enhanced Raman scattering, discussed in Sec- tion 1.3, is another popular non-invasive sensing option. A thorough review of SERS is beyond the scope of this colloquium, hence we refer the interested reader to the following articles [95,96,199–202]. Here we will be focussing on SERS relevant structures produced using plasma methods, rather than top-down lithographic approaches. Agarwal et al. [199] fabricated Ag and Au nanoparticle substrates using pulsed laser ablation demonstrating a reasonable de- Fig. 6. (a) The effect of nanoparticle shape on the fraction of incident light scattered into the photoactive layer of the so- gree of control over the bottom-up growth through vari- lar cell. Reprinted with permission from [180], copyright 2008, ation of the chamber pressure and the number of pulses American Institute of Physics. The maximum enhancement and with a clear SERS response for Rhodamine 6G [199]. possible for various materials with (b) radius and (c) surface Rider et al. [148] recently used a plasma-based approach coverage, where Re[ε(ω)] is the real part of the nanoparticle to grow metal nanoparticles in combination with verti- permittivity. (b) and (c) reprinted with permission from [178], cal graphenes to make 3D metal-graphene nanohybrid copyright 2010, American Institute of Physics. SERS platforms (see Fig. 7). It was demonstrated that using vertical graphenes, rather than horizontal graphenes, provides a markedly higher effective bookshelf like area where Au nanoparticles can attach. This means that there sensors work on the basis that an analyte/biomolecule changes the local refractive index in the vicinity of the is a much greater area where analyte species can at- surface of the metallic film. This in turn changes the reso- tach, compared to typical horizontal SERS sensor archi- tectures [148]. nance of the surface plasmons which can be detected either as a change in angle or change in wavelength of absorp- Biomedicine and the convergence of plasmonics tion. Sensors working on this principle typically use the and plasmas: an example of a biomedical application Kretschman configuration to excite the surface plasmons (excluding sensors) which involves plasmons is photother- (see Fig. 4e). Examples include Wu et al. [189], where mal therapy [170,203–205](seeFig.5c). The nanoparticle a change in biomolecule concentration led to a change (often Au, Au-nanoshells and variations) is excited in vivo in refractive index near the metal surface which leads to with light at the resonant frequency of the particle. This change in propagation constant of the SPP which can be serves to excite LSPs, which are then dissipated thermally measured by attenuated total internal reflection. Commer- in the local medium possibly killing the surrounding cells. cially available sensors based on SPR such as the BIAcore For example, hollow Au nanoparticles were functionalized instrument from Pharmacia have been widely used for a with an antibody/ligand that would dock on to an anti- number of decades [190–192]. Another example is a hand- gen present on the surface of a cancer cell. The area would held SPR biosensor [193] which could detect changes as be exposed to EM radiation that would cause a plasmon . × −6 low as 3 3 10 refractive index units. Localized surface to be generated from the NP, which would lead to heat plasmon resonance (LSPR) [8,194–197] sensors work on a released locally which would selectively kill the cancer similar principle, although the change measured is wave- λ cell and leave the surrounding tissue unaffected [206]. It length only, not angle. The change in wavelength, as a has recently been shown that charged nanoparticles can result of absorbtion of a biospecies is [8]: be less toxic [207], moreover, using plasmas provides a high level of control over the charge and transport of Δλmax = nbulk Δn [1 − exp(−2d/ld)] , (21) nanoparticles [208]. Page 14 of 19 Eur. Phys. J. D (2012) 66: 226

that plasma-based fabrication is a relatively safe method for the production of a range of nanomaterials [216].

4.4 Some further links between plasmas and plasmons

Let us now discuss more explicit links between plasma and plasmonic phenomena. Wang et al. [2] recently noted that the plasma screening effect (a fundamental, generic plasma property) leads to bandgap opening for bulk plasmons both in gaseous plasmas and metal plasmas. When an electromagnetic (EM) wave is incident on an inter- face between a plasma and a dielectric (e.g. vacuum), a charge displacement leads to the excitation of forward and backward plane waves. The screening happens below the plasma frequency when the plane waves destructively interfere with the incident EM wave creating an energy gap. Above the plasma frequency, the forward plane wave changes phase and constructively interfere with the incoming EM wave. This is now the transverse bulk plasmon [2] (see also the definition in Sect. 1.2). It should be noted that the bandgap is determined by the plasma density, i.e. the denser the plasma, the wider the bandgap. This property is very useful to determine (and tailor) the bandgap for specific types of propagating plasmons in materials. Separating plasma-specific (e.g. energy absorption near plasmon resonance) and other (e.g., non-resonant) phenomena in plasmonic responses is also critical in op- timising the performance of a range of devices, in particular, solar cells [185]. Comparison of silver (i.e. resonant in visible regime) and aluminium (i.e. non resonant in the visible regime) nanoparticles showed that they interact with incoming light differently. Aside from the “normal” scattering from nanoparticle geometric features including surface roughness, etc., resonant nanoparticles (i.e., sil- Fig. 7. (a) Au nanoparticle decorated vertical graphenes and −2 ver) have the added complication of parasitic absorption a SERS spectra of 10 M 4-aminothiophenol deposited on Au decorated vertical graphenes; (b) concept of Au decorated around the plasmon resonance. This resonance, however, vertical graphenes as a bookshelf-style sensor. (a) and (b) can be shifted by modifying the height:radius ratio. De- from [148] – reproduced by permission of The Royal Society of pending on the nanoparticle material, and whether they Chemistry. are subject to any plasma-specific effects, the nanoparticle geometry will have to be modified to effect the best device performance. Moreover, study of plasmonic coupling, resonance frequencies etc. will facilitate plasma nanofab- Moving slightly away from nanoplasmonics, there has rication efforts to produce structures deterministically to been a lot of excitement in the last few years centred optimize device response. Studying nanoscale plasma phe- around the use of atmospheric plasmas in medicine and nomena in plasmonic nanostructures should improve pre- health care [209]. Specific applications include (but are dictability of responses of nanophotonic devices which si- not limited to): wound treatment, tissue engineering [209], multaneously use plasma and non-resonant optical effects. treatment of skin diseasessuchasRosacea[210], antimi- Although these studies in many cases require quantum crobial applications [211], inducing cancer cell apopto- treatment, they will still be able to draw on the physics sis [212] and minimizing adenovirus infectivity [213]. In of collective phenomena in gas plasmas as foundation. particular, it has also been recently shown that cold plas- Another analogy between plasmonics and plasma mas may be used to selectively kill cancer cells with- physics can be drawn, by examining electron-surface scat- out damaging surrounding healthy cells [214]. Kong et al. tering. As discussed in Section 3, Mie scattering the- noted that the synergies between cold atmospheric plas- ory may be used to describe how nanoparticles of dif- mas and charged nanoparticles addressed the issues of re- ferent sizes interact with and scatter light. However, we activity, selectivity, toxicity and penetration required for stress that this is a geometric effect, not a plasma effect. effective drug delivery and medical treatment [208]. Also The scattering of electrons from a surface, causes a size- important to note is the issue of nanosafety. A recently introduced collisionality in the plasma. This collisionality published review on plasmas and nanosafety [215] suggests is included in the model for plasmonic nanoshells which Eur. Phys. J. D (2012) 66: 226 Page 15 of 19 incorporated an electron surface scattering term in the 1016 cm−3, plasmonic responses could be expected in the dielectric constant [84]: as yet elusive THz range [218]. Another link between plasma physics and plasmonics ω2 ω2 is also possible – namely, using the emission from plas- ε ε − p p , C = exp + mas to excite plasmons. Using plasmas as an excitation ω(ω + i[γintra + γ(LB)]) ω(ω + iγintra ) (22) source would potentially enable use of the same source to excite IR-VIS-UV plasmons requiring only simple tun- where εexp is the experimental dielectric constant, γ = ing of the plasma parameters. It is an attractive research γintra + γ(LB) is the mean free path dependant damping, area – both in terms of the pure physics involved as well γ(LB)=VF /LB is the damping due to surface scattering as applications. Thus it is an area that the authors of this where VF is the Fermi velocity, LB isthemeanfreepathof the electrons in the cell and γintra is the intraband damp- colloquium are currently investigating and the results will ing term [84]. The size of the nanoparticles is important be reported elsewhere. 3 3 2 2 It appears that as the fields of plasmonics and plasma for LB which is equal to (4(r −r ))/(3(r +r )), where r0 0 i 0 i nanoscience further develop there will be a likely common and ri are the outer and inner radii, respectively. The specific material and geometry of the nanoparticle determine ground – not only in terms of fabrication and fundamental the contribution of surface scattering correction to dielec- physics, but in real world, complementary applications in tric permittivity [84]. For example, the surface scattering many fields. If an integrated approach which recognises term is particularly important for thin shells causing a the common physical foundations and similarities in the blue shift of the resonance. By taking this surface scat- many physical phenomena is used, many new interesting tering term into account, one can tailor nanoarrays (and effects may be discovered which in turn may lead to new nanoplasmas) to achieve the resonant responses required. applications in several fields. A similar size-introduced collisionality effect is observed for discharge boundaries in gaseous microplasmas when the size of the discharge is reduced to submillimeter 5 Conclusions and outlook for future and even smaller dimensions [217]. The transition from a bulk plasma to a microplasma (typically at micrometre synergistic research in the field and submicrometre sizes) with size dependant properties occurs at a critical size determined by [217]: To summarise, in this colloquium we have presented a slice of two quite distinct fields – plasma physics and plasmon- – surface to volume ratio (SVR); ics, connected by very similar physics, in particular, the – electrode spacing (ES) notion of collective plasma waves and oscillations. We have presented the essential equations of each field and demon- which is very similar to nanoplasmonic arrays. strated their similarities and placed them firmly within As the SVR increases and ES decreases, the electron the historical field. We then used the research field of temperature and density increase, which in turn affects the Plasma Nanoscience to show that these similarities are collision rates in the plasma and hence the plasma char- not merely academic, but can be put into practice in the acteristics. Similarly, scattering from the boundaries does design of plasma-aided fabrication of nanoplasmonic ar- affect collisionality and equilibrium of gaseous plasmas, rays for a myriad of applications from sensors to photo- although at different time scales and involving different voltaic cells. We also discussed emerging biomedical ap- species (atoms/molecules rather than electrons). Such dis- plications in both plasmonics and atmospheric plasmas charges are still too large for electron scattering effects to which both contribute to the field of cancer treatment – become as important as in plasmonics. However, gaseous by recognising the link between plasmonics and plasmas plasma discharges and plasma collective phenomena are in emergent fields such as cancer research, novel treat- strongly affected by secondary electron emission from the ments and techniques using the best of both fields may surface. It is presently unclear if this effect plays a role in be further developed. Indeed, as device design matures plasmonics. Nevertheless, the similarity remains and could we will have increasing opportunity to study nanoplasmas prove useful to note at a later juncture. and nanoplasma phenomena. Hence, by reaching back as Moreover, in a contribution to the recently published far as primordial earth (for terrestrial gaseous plasmas) 2012 Plasma Roadmap [218], Tachibana notes that mi- and the 4th century AD (for plasmons in solid plasmas) croplasma arrays can be used just like a photonic crystal. and looking forward to the state-of-the-art nanomedical They note by examining the permittivity [218]: and technological advances, one concludes that everything old, is ultimately, new once again. ω2 A list of symbols and abbreviations used in the collo- ε − p , p =1 2 (23) quium is provided in Table 2 ω (1 + iνm/ω) where νm is the electron collision frequency, all other sym- A.E.R acknowledges support from the CSIRO OCE Postdoc- bols defined as before, that the plasma density and the toral Fellowship Program. This work was partially supported plasmon frequency (ωp) is what will ultimately affect the by the Australian Research Council, CSIRO OCE Science response of the ’array’. Given a plasma density of around Leader Program and CSIRO Sensors & Sensor network TCP. Page 16 of 19 Eur. Phys. J. D (2012) 66: 226

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